SOLUTION: | cosQ sinQ 0| A= |-sinQ cosQ 0| | 0 0 1| is invertible for all Q ,the find A^-1.

Algebra ->  College  -> Linear Algebra -> SOLUTION: | cosQ sinQ 0| A= |-sinQ cosQ 0| | 0 0 1| is invertible for all Q ,the find A^-1.      Log On


   

Question 1044593: | cosQ sinQ 0|
A= |-sinQ cosQ 0|
| 0 0 1|
is invertible for all Q ,the find A^-1.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The rows (or columns) of A constitute an orthonormal set of vectors (i.e., any pair is orthogonal, or has scalar product 0; and each has magnitude 1.)
Therefore the inverse of A will just be its transpose A%5ET.
===> .
Feel free to verify that A%2AA%5ET+=+A%5ET%2AA+=+I%5B3%5D.